Rafferty received a life sentence after he was found guilty of first-degree murder, sexual assault causing bodily harm and kidnapping following his 2½ month trial in a London courthouse earlier this year.
In the document, filed with the Court of Appeal of Ontario on July 26, Rafferty says "the jury failed to apprehend the evidentiary requirement to convict for first-degree murder." He also says Justice Thomas Heeney failed to properly instruct the jury.
Rafferty also writes that he missed the 30-day deadline to appeal because he had difficulty accessing a telephone to contact legal counsel.
Rafferty says he would prefer a trial by jury, if a second trial is ordered.
The application appears to have been filed from Kingston Penitentiary.
Rafferty was found guilty on May 11 after more than a day of deliberations but Justice Heeney was criticized for excluding certain character evidence collected by the police, including that Rafferty had used his computer to search for child pornography.
That information was deemed inadmissible because police failed to get proper search warrants when accessing data on Rafferty’ laptop.
Tori's remains found under rocks
Tori disappeared after leaving her elementary school in Woodstock on April 8, 2009, prompting police to launch a massive search effort including hundreds of officers and volunteers. Her partially clothed remains were found more than three months later under a pile of rocks in Mount Forest, Ont., 100 kilometres north of her home.
Much of Rafferty's trial centred on the prosecution's star witness Terri-Lynne McClintic, who pleaded guilty to the first-degree murder of Tori in April 2010.
McClintic told jurors she lured Tori to Rafferty's car on his orders. The pair then drove the girl first to Guelph and later to rural area outside Mount Forest. McClintic said she killed Tori with a hammer after Rafferty raped the young girl, contradicting previous statements she made to police that he was the one who delivered the fatal blows.
The pair were arrested a month after the Grade 3 student disappeared but McClintic agreed to help investigators a short time later.
Rafferty's trial, which began on March 5, was mostly taken up by the Crown's case including 61 witnesses and almost 200 exhibits. Defence lawyer Dirk Derstine took just one day to present evidence.
Rafferty did not testify
Derstine maintained that Rafferty had simply been a horrified spectator to Tori's abduction by McClintic. He said she had killed the girl unbeknownst to him.
Rafferty did not testify in his own defence but did rise to speak during his sentencing hearing on May 15.
He said he was sorry for Tori's death but disagreed with his conviction.
"I am guilty of many crimes and there are a lot of things I am very, very ashamed of but these three counts, I still stand firmly behind not guilty," he said.
During the sentencing hearing, Justice Heeney called Rafferty a "monster" and defended his decision to exclude the character evidence, saying that doing otherwise would have demonstrated a "fundamental misunderstanding" of the basic concepts of Canadian law.
Heeney said character evidence has unduly influenced juries in the past.
Rafferty also received 10 years each for kidnapping and sexual assault causing bodily harm, to be served concurrently with the life sentence for first-degree murder.